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JEE Main 2021 (25 Feb, Shift 2) · Spring Systems

Spring Systems question from JEE Main 2021 (25 Feb, Shift 2)

Q65JEE Main 2021 · 25 FEB · SHIFT 2Easy

Spring Systems

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is:

Figure

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Answer: (b)

  1. Springs on both sides of the block act in parallel: keff=2k+2k=4kk_{eff} = 2k + 2k = 4k.
  2. T=2πm4k=πmkT = 2\pi\sqrt{\frac{m}{4k}} = \pi\sqrt{\frac{m}{k}}
  3. So the answer is (b) πmk\pi\sqrt{\frac{m}{k}}.
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